**Finding the Vertex of a Parabolic Equation**This exercise involves determining the vertex of the quadratic equation:\[ y = -0.28x^2 - 1.0x + 2.1 \]### Steps to Find the Vertex:1. **Identify the coefficients**: - \( a = -0.28 \) - \( b = -1.0 \) - \( c = 2.1 \)2. **Use the vertex formula**: The x-coordinate of the vertex can be found using the formula: \[ x = -\frac{b}{2a} \]3. **Calculate the x-coordinate**: \[ x = -\frac{-1.0}{2 \times -0.28} = -\frac{1.0}{-0.56} = 1.79 \]4. **Calculate the y-coordinate**: Substitute \( x = 1.79 \) back into the equation to find the y-coordinate: \[ y = -0.28(1.79)^2 - 1.0(1.79) + 2.1 \] \[ y \approx -0.28(3.2041) - 1.79 + 2.1 \] \[ y \approx -0.897 + 2.1 - 1.79 \] \[ y \approx -0.587 \]Thus, the vertex of the parabola \( y = -0.28x^2 - 1.0x + 2.1 \) is approximately at \( (1.79, -0.587) \).### Explanation:The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. In this case, since \( a = -0.28 \) is negative, the parabola opens downwards indicating the vertex is the maximum point.

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Answered: find the vertex 4==.28x2-1LOX+2.1

Math

Algebra

find the vertex 4==.28x2-1LOX+2.1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Finding the Vertex of a Parabolic Equation**

This exercise involves determining the vertex of the quadratic equation:

\[ y = -0.28x^2 - 1.0x + 2.1 \]

### Steps to Find the Vertex:
1. **Identify the coefficients**:
- \( a = -0.28 \)
- \( b = -1.0 \)
- \( c = 2.1 \)

2. **Use the vertex formula**:
The x-coordinate of the vertex can be found using the formula:

\[ x = -\frac{b}{2a} \]

3. **Calculate the x-coordinate**:
\[ x = -\frac{-1.0}{2 \times -0.28} = -\frac{1.0}{-0.56} = 1.79 \]

4. **Calculate the y-coordinate**:
Substitute \( x = 1.79 \) back into the equation to find the y-coordinate:

\[ y = -0.28(1.79)^2 - 1.0(1.79) + 2.1 \]
\[ y \approx -0.28(3.2041) - 1.79 + 2.1 \]
\[ y \approx -0.897 + 2.1 - 1.79 \]
\[ y \approx -0.587 \]

Thus, the vertex of the parabola \( y = -0.28x^2 - 1.0x + 2.1 \) is approximately at \( (1.79, -0.587) \).

### Explanation:
The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. In this case, since \( a = -0.28 \) is negative, the parabola opens downwards indicating the vertex is the maximum point.

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